- journal article metadata
European Mathematical Society Publishing House
2018-06-03 23:30:01
Commentarii Mathematici Helvetici
Comment. Math. Helv.
CMH
0010-2571
1420-8946
General
10.4171/CMH
http://www.ems-ph.org/doi/10.4171/CMH
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Swiss Mathematical Society
93
2018
2
Rigidity and flexibility for handlebody groups
Sebastian
Hensel
Universität Bonn, Germany
Mapping class groups, handlebody groups, commensurator, rigidity
We show that finite index subgroups of the handlebody group are rigid in their ambient mapping class group: any injective map of a finite index subgroup of the genus $g$ handlebody group into the genus $g$ mapping class group is conjugation by a mapping class group element. On the other hand, we construct an injection of the genus $g$ handlebody group into a genus $h > g$ mapping class group which is not conjugate into a handlebody group.
Manifolds and cell complexes
Group theory and generalizations
335
358
10.4171/CMH/436
http://www.ems-ph.org/doi/10.4171/CMH/436
5
31
2018